A rehabilitation center research was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful reha- bilitation.

A rehabilitation center research was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful reha- bilitation. Patient records in the rehabilation center were examined, and 24 male subjects ranging in age from 18 to 30 years had undergone simi- lar corrective knee surgery during the past year were selected for the study. The number of days required for succesful completion of physical therapy and the prior physical fitness status (below average, average, above average, etc.) for each patient follows: Observation (j) Pre-surgery status 1 2 2 3 4 5 6 7 8 9 10 Poor 44 38 43 48 44 47 42 45 45 43 Below Average 29 42 38 40 43 40 30 42 Average 30 35 39 28 31 31 29 35 29 33 Above Average 26 32 21 20 23 22 Excellent 14 18 22 21 17 20 20 28 (a) Suppose that we wish to determine whether or not the mean rehabil- itation time in patients with a 'Poor' or "Below Average' pre-surgery health status is different from the mean rehabilitation time in patients in any of the other pre-surgery groups. State the appropriate null and alternative hypothesis for this question.(b) Carry out a test of the hypothesis stated in (a). State what test statistic you are using, and provide all the necessary information used to cal- culate the test statistic (e.g. show ALL your work). Report the value of the test statistic, calculate the p-value, state your decision, and in- terpret the results of your test in a way that would be understandable to a non-statician. (c) Form simultaneous 95% confidence intervals for the difference in the mean rehabilation time of: i. patients with a 'Poor' pre-surgery health status versus that a pa- tients with a ' Average' pre-squrger health status; ii. patients with a 'Poor' pre-surgery health status versus that a pa- tients with a 'Above Average' pre-squrger health status; iii. patients with a 'Poor' pre-surgery health status versus that a pa- tients with a 'Excellent" pre-squrger health status